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On the nature of certainty equivalent functionals

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  • Hennessy, David A.
  • Lapan, Harvey E.

Abstract

We explore connections between the certainty equivalent return (CER) functional and the underlying utility function. Curvature properties of the functional depend upon how utility function attributes relate to Hyperbolic Absolute Risk Aversion (HARA) type utility functions. If the CER functional is concave, i.e., if risk tolerance is concave in wealth, then preferences are standard. The CER functional is linear in lotteries if utility is HARA and lottery payoffs are on a line in state space. Implications for the optimality of portfolio diversification are given. When utility is concave and Non-increasing Relative Risk Averse, then the CER functional is superadditive in lotteries. Depending upon the nature of covariation among lottery payoffs, CERs for Constant Absolute Risk Averse utility functions may be subadditive or superadditive in lotteries. Our approach lends itself to straightforward experiments to elicit higher order attributes on risk preferences.
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  • Hennessy, David A. & Lapan, Harvey E., 2006. "On the nature of certainty equivalent functionals," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 1-10, December.
    • Handle: RePEc:eee:mateco:v:43:y:2006:i:1:p:1-10
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    2. Hennessy, David A. & Lapan, Harvey E., 2006. "On the nature of certainty equivalent functionals," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 1-10, December.
    3. Luigi Guiso & Monica Paiella, 2008. "Risk Aversion, Wealth, and Background Risk," Journal of the European Economic Association, MIT Press, vol. 6(6), pages 1109-1150, December.
    4. Suen, Richard M. H., 2022. "Precautionary Saving Behaviour under Ambiguity," MPRA Paper 114382, University Library of Munich, Germany.
    5. Loïc Berger & Johannes Emmerling, 2020. "Welfare As Equity Equivalents," Journal of Economic Surveys, Wiley Blackwell, vol. 34(4), pages 727-752, September.
    6. Moris S. Strub & Xun Yu Zhou, 2021. "Evolution of the Arrow–Pratt measure of risk-tolerance for predictable forward utility processes," Finance and Stochastics, Springer, vol. 25(2), pages 331-358, April.
    7. Colin Lizieri & Gianluca Marcato & Paul Ogden & Andrew Baum, 2012. "Pricing Inefficiencies in Private Real Estate Markets Using Total Return Swaps," The Journal of Real Estate Finance and Economics, Springer, vol. 45(3), pages 774-803, October.
    8. Bui, Dien Giau & Hasan, Iftekhar & Lin, Chih-Yung & Zhai, Rui-Xiang, 2022. "Income, trading, and performance: Evidence from retail investors," Journal of Empirical Finance, Elsevier, vol. 66(C), pages 176-195.

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